FILTR: Extracting Topological Features from Pretrained 3D Models
This work provides a first data-driven method to extract persistence diagrams from raw point clouds via pretrained encoders, enabling efficient topological feature extraction for downstream tasks.
The authors investigate whether topological information can be derived from features of pretrained 3D point cloud encoders. They introduce DONUT, a synthetic benchmark, and FILTR, a learnable framework that predicts persistence diagrams from frozen encoders, showing that existing encoders retain limited topological signals but FILTR can approximate diagrams.
Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been shown to provide informative summaries of a shape's multiscale structure. In this paper we pose the question whether topological information can be derived from features produced by 3D encoders. To address this question, we first introduce DONUT, a synthetic benchmark with controlled topological complexity, and propose FILTR (Filtration Transformer), a learnable framework to predict persistence diagrams directly from frozen encoders. FILTR adapts a transformer decoder to treat diagram generation as a set prediction task. Our analysis on DONUT reveals that existing encoders retain only limited global topological signals, yet FILTR successfully leverages information produced by these encoders to approximate persistence diagrams. Our approach enables, for the first time, data-driven extraction of persistence diagrams from raw point clouds through an efficient learnable feed-forward mechanism.